Estimating Greeks in simulating Lévy-driven models

Abstract

We develop methods for estimating price sensitivities by simulation for Levydriven models. The methods combine pathwise derivatives and likelihood ratio method estimators with alternative approaches to approximating and simulating Levy processes. We develop estimators based on exact sampling of increments, time-change representations of Levy processes, saddlepoint approximations to the score functions of the increments, compound Poisson approximations and compound Poisson approximations with Brownian approximations to small jumps. We discuss the relative merits of these various alternatives, both in theory and in practice, and we illustrate their use through examples.